Mathematics Pacing Resource Document
5.AT.4
Standard: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions
(e.g., by using visual fraction models and equations to represent the problem).
Teacher Background Information:
The concept unit fraction is a fraction that has a one in the denominator. For example, the fraction 3/5 is 3 copies of the unit fraction 1/5. 1/5 + 1/5
+ 1/5 = 3/5 = 1/5 x 3 or 3 x 1/5.
Example:
Knowing the number of groups/shares and finding how many/much in each group/share
Four students sitting at a table were given 1/3 of a pan of brownies to share. How much of a pan will each student get if they share the pan of
brownies equally?
The diagram shows the 1/3 pan divided into 4 equal shares with each share equaling 1/12 of the pan.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Standard: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions
(e.g., by using visual fraction models and equations to represent the problem).
Teacher Background Information:
This standard asks students to work with story contexts where a unit fraction is divided by a non-zero whole number. Students should use various
fraction models and reasoning about fractions.
Example:
You have 1/8 of a bag of pens and you need to share them among 3 people. How much of the bag does each person get?
Student 2
I drew a rectangle and divided it into 8 columns to represent my 1/8. I shaded the first column. I then
needed to divide the shaded region into 3 parts to represent sharing among 3 people. I shaded one-third
of the first column even darker. The dark shade is 1/24 of the grid or 1/24 of the bag of pens.
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/3
1/3
Student 3
1/8 of a bag of pens divided by 3
people. I know that my answer will be
less than 1/8 since I’m sharing 1/8
into 3 groups. I multiplied 8 by 3 and
got 24, so my answer is 1/24 of the
bag of pens. I know that my answer is
correct because (1/24) x 3 = 3/24
which equals 1/8.
1/3
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Standard: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions
(e.g., by using visual fraction models and equations to represent the problem).
Teacher Background Information:
Example:
Create a story context for 5 ÷ 1/6. Find your answer and then draw a picture to prove your answer and use multiplication to reason about whether your
answer makes sense. How many 1/6 are in 5?
Student
The bowl holds 5 Liters of water. If we use a scoop that holds 1/6 of a Liter, how many scoops will we need in order to fill the entire
bowl?
I created 5 boxes. Each box represents 1 Liter of water. I then divided each box into sixths to represent the size of the scoop. My
answer is the number of small boxes, which is 30. That makes sense since 6 x 5 = 30.
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 a whole has 6/6 so five wholes would be 6/6 + 6/6 + 6/6 + 6/6 + 6/6 =30/6
Example:
How many 1/3-cup servings are in 2 cups of raisins?
Student:
I know that there are three 1/3 cup servings in 1 cup of raisins. Therefore, there are 6 servings in 2 cups of raisins. I can also
show this since 2 divided by 1/3 = 2 x 3 = 6 servings of raisins.
Examples:
Knowing how many in each group/share and finding how many groups/shares
Angelo has 4 lbs. of peanuts. He wants to give each of his friends 1/5 lb. How many friends can receive 1/5 lb. of peanuts? A diagram for 4 ÷ 1/5 is
shown below. Students explain that since there are five fifths in one whole, there must be 20 fifths in 4 lbs.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Standard: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions
(e.g., by using visual fraction models and equations to represent the problem).
Teacher Background Information:
Example:
How much rice will each person get if 3 people share 1/2 lb of rice equally?
A student may think or draw ½ and cut it into 3 equal groups then determine that each of those part is 1/6.
A student may think of ½ as equivalent to 3/6. 3/6 divided by 3 is 1/6.
Process Standards to Emphasize with Instruction of 5.AT.4:
5.PS.1: Make sense of problems and persevere in solving them.
5.PS.2: Reason abstractly and quantitatively.
5.PS.3: Construct viable arguments and critique the reasoning of others.
5.PS.4: Model with mathematics.
5.PS.5: Use appropriate tools strategically.
5.PS.6: Attend to precision.
5.PS.7: Look for and make use of structure.
5.PS.8: Look for and express regularity in repeated reasoning.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Standard: 5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions
(e.g., by using visual fraction models and equations to represent the problem).
Lesson Plans/Print Activities:

Math Expressions Resources:
o Unit 9: Lesson 10
o Unit 9: Lesson 11
o Unit 9: Lesson 12

https://www.engageny.org/resource/grade-5-mathematics-module-6topic-e-lesson-21 Multi-Step Word Problems Lessons (Lessons 21-26)

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-g-overview (Lessons 25-31)

https://www.illustrativemathematics.org/illustrations/1196 Illustrative
Math Task

https://grade5commoncoremath.wikispaces.hcpss.org/file/view/Dividing
_with_Unit_Fractions_GA_5nf7.pdf/407299828/Dividing_with_Unit_Fract
ions_GA_5nf7.pdf Dividing Unit Fractions Lessons

http://fractionbars.com/CommonCore/Gd5Les/CCSSDiv5_NF_7aGd5.pdf
Division of unit fractions by whole numbers lesson.

http://www.mathsolutions.com/documents/Fifth_Grade_Lesson.pdf
Math Solutions Lesson
Indianapolis Public Schools
Web-based Practice:

https://learnzillion.com/student/lessons/3788 Divide whole
numbers by unit fractions and unit fractions by whole numbers:
LZ3788, LZ3787, LZ3786

http://www.basic-mathematics.com/dividing-fractions-wordproblems.html Online examples

http://www.homeschoolmath.net/online/problem_solving.php List
of problem solving websites
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
1) A farmer mows one-fifth of an acre each day. If his property has three acres, how many days will it take to mow it all? [Delaware Dept. of Education]
A. 3 days
B. 5 days
C. 8 days
D. 15 days Answer: D
1
a bag of licorice to share with her friends. She decided to share the
8
contents of the licorice bag equally with her teammates Sara and Jessica. How much of the licorice bag will each girl receive?
1
[Delaware Dept. of Education (modified)] Answer:
of the original bag of licorice
24
2) Tara had a great soccer game! After the soccer game, the coach awarded Tara
3)


3 pineapples
1
1 serving =
pineapple
2
1
would be the method of solution.
2
[NAEP, 2005, Grade 8 Mathematics Assessment] Sample Answer: Samantha has 3 pineapples. She figures that each person will eat half of a pineapple. How
many people can Samantha serve with the 3 pineapples?
Given the information above, write a mathematics word problem for which 3 ÷
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
4) Students are running in a relay race. Each team will run a total of 2 miles. Each member of a team will run
1
of a mile. How many students will a team need
5
to complete a race? Choose the correct number. You may use the number line to help find your answer.
[Smarter Balanced sample items] Answer: 10 students
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
(5.AT.3)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
(Readiness I)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.AT.4
Item Bank:
Indianapolis Public Schools
Curriculum and Instruction